This document discusses algorithms and analysis of algorithms. It covers key concepts like time complexity, space complexity, asymptotic notations, best case, worst case and average case time complexities. Examples are provided to illustrate linear, quadratic and logarithmic time complexities. Common sorting algorithms like quicksort, mergesort, heapsort, bubblesort and insertionsort are summarized along with their time and space complexities.
This is the second lecture in the CS 6212 class. Covers asymptotic notation and data structures. Also outlines the coming lectures wherein we will study the various algorithm design techniques.
PPT on Analysis Of Algorithms.
The ppt includes Algorithms,notations,analysis,analysis of algorithms,theta notation, big oh notation, omega notation, notation graphs
Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.
For further information
https://github.com/ashim888/dataStructureAndAlgorithm
References:
https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/asymptotic-notation
http://web.mit.edu/16.070/www/lecture/big_o.pdf
https://rob-bell.net/2009/06/a-beginners-guide-to-big-o-notation/
https://justin.abrah.ms/computer-science/big-o-notation-explained.html
Introduction to Algorithms and Asymptotic NotationAmrinder Arora
Asymptotic Notation is a notation used to represent and compare the efficiency of algorithms. It is a concise notation that deliberately omits details, such as constant time improvements, etc. Asymptotic notation consists of 5 commonly used symbols: big oh, small oh, big omega, small omega, and theta.
Algorithms Lecture 1: Introduction to AlgorithmsMohamed Loey
We will discuss the following: Algorithms, Time Complexity & Space Complexity, Algorithm vs Pseudo code, Some Algorithm Types, Programming Languages, Python, Anaconda.
Data Structures, which is also called as Abstract Data Types (ADT) provide powerful options for programmer. Here is a tutorial which talks about various ADTs - Linked Lists, Stacks, Queues and Sorting Algorithms
This is the second lecture in the CS 6212 class. Covers asymptotic notation and data structures. Also outlines the coming lectures wherein we will study the various algorithm design techniques.
PPT on Analysis Of Algorithms.
The ppt includes Algorithms,notations,analysis,analysis of algorithms,theta notation, big oh notation, omega notation, notation graphs
Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.
For further information
https://github.com/ashim888/dataStructureAndAlgorithm
References:
https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/asymptotic-notation
http://web.mit.edu/16.070/www/lecture/big_o.pdf
https://rob-bell.net/2009/06/a-beginners-guide-to-big-o-notation/
https://justin.abrah.ms/computer-science/big-o-notation-explained.html
Introduction to Algorithms and Asymptotic NotationAmrinder Arora
Asymptotic Notation is a notation used to represent and compare the efficiency of algorithms. It is a concise notation that deliberately omits details, such as constant time improvements, etc. Asymptotic notation consists of 5 commonly used symbols: big oh, small oh, big omega, small omega, and theta.
Algorithms Lecture 1: Introduction to AlgorithmsMohamed Loey
We will discuss the following: Algorithms, Time Complexity & Space Complexity, Algorithm vs Pseudo code, Some Algorithm Types, Programming Languages, Python, Anaconda.
Data Structures, which is also called as Abstract Data Types (ADT) provide powerful options for programmer. Here is a tutorial which talks about various ADTs - Linked Lists, Stacks, Queues and Sorting Algorithms
Variants of Support Vector
Machines (SVM) were employed for classification and also
compared the results with Multi-layered Perceptron (MLP).
Empirical results show that both SVM and MLP were suitable
for such motor imagery classifications with the accuracies 85%
and 85.71% respectively. Among all employed feature extraction
techniques wavelet-based methods specifically the energy-
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Vaccine management system project report documentation..pdfKamal Acharya
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This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
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using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
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Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
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Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...
Data Structure: Algorithm and analysis
1. DATA STRUCTURES
ALGORITHM AND ANALYSIS
Rajdeep Chatterjee
Assistant Professor
School of Computer Engineering
KIIT University
2. OVERVIEW
Algorithm
Analysis of Algorithm
Space Complexity
Time Complexity
Step Counts
Asymptotic Notations
Big-oh Notations
Rate of Growth
Types of Time Complexity
Best Case Complexity
Worst Case Complexity
Average Case Complexity
3. ALGORITHM
Algorithm is a finite set of well defined
computational instructions written in a proper
sequence in order to solve a problem.
Criteria-
Input
Output
Definiteness
Finiteness
Effectiveness
4. EXAMPLES
ADD: INTEGER a, b, c
1. Read a & b
2. add a & b
3. store the sum of a & b to c
4. print c
In C, exp(1)
void add(int a, int b){
int c;
c=a+b;
printf(“%d”,c);
}
In C, exp(2)
int add(int a, int b){
int c;
c=a+b;
return c;
}
5. ANALYZING AN ALGORITHM
Why is it important?
Predict the feasibility requirement of your code
(algorithm).
Usual requirements
Execution time
Memory space
The complexity of the algorithm is determined in
terms of space and time.
Space complexity ← execution time
Time complexity ← memory space
6. SPACE COMPLEXITY
Amount of computer memory required during
program execution.
Instruction space – space required to store the
code.
Fixed space requirement – input independent
Variable space requirement – input dependent
S = F(I) otherwise S = C
7. EXAMPLES
Exp(1)
int main(){
printf(“KIIT UNIVERSITY”);
}
Exp(2)
void bubble(int a[], int n){
int i,j;
for(i=0;i<n-1;i++){
for(j=0;j<n-1-i;j++)
if(a[j]>a[j+1])
swap (a[j],a[j+1])
}
}
8. TIME COMPLEXITY
The amount of computer time that it needs to run
to completion.
It is determined without considering the following
information-
The machine we are executing,
Its machine language instruction set,
The time required by each machine instruction,
The translation, a compiler/interpreter will make from
the source code to machine language.
9. EXAMPLES
Exp(1)
x=x+1;
Exp(2)
for(i=1 ; i<=n ; i++)
x=x+1;
Exp(3)
for(i=1 ; i<=n ; i++)
for(j=1 ; j<=n ; j++)
x=x+1;
Our concern should be the order of magnitude/ growth of an algorithm
for an input n.
Exp(4)
int main(){
printf(“KIIT UNIVERSITY”);
}
14. ASYMPTOTIC NOTATIONS
O (Big-oh) Notation
Consider a function f(n) which is non-negative for all
integers n=0. we say that f(n)is Big-oh g(n), which we
write f(n)=O(g(n)), if there exits an integer n0 and a
constant c>0 such that for all integers n=n0, f(n)=cg(n).
In other words,
O(g(n))={f(n): ∃ positive constants c and n0 ∋ 0 ≤ f(n) ≤cg(n) ∀ 𝑛 ≥ 𝑛0 }
O-notation to give an upper bound on a function to within a
constant factor.
15. EXAMPLE
Two students, X & Y
Let, performance of X & Y are TX and TY respectively,
Conclusion is for a large n, TX(n) ≻ TY(n)
So, who is a better professional ?
Ans. X
When X outperforms Y and by what factor ?
Ans. n0 and c
# Events X Y TX ∼ TY
1 10th 70% 85% TX(1) ≺ TY(1)
2 (10+2)th 65% 78% TX(2) ≺ TY(2)
3 B.Tech 8.8 cgpa 8.7 cgpa TX(3) ≻ TY(3)
4 M.Tech GATE rank 120 GATE rank 1700 TX(4) ≻ TY(4)
5 Ph.D 5 publications 2 publications TX(5) ≻ TY(5)
6 Job 20 lakhs/p.a. 10 lakhs/p.a. TX(6) ≻ TY(6)
16. EXAMPLE
Suppose C=1 then, f(n)=6n+135
f(n) = cn2
6n +135 = cn2 = n2 (since c=1)
0 = n2 - 6n -135
0 = (n-15)(n+9)
Since (n+9) > 0 for all values n ≥ 0, then (n-15)=0
n0=15
Find n0 when c=2 & c=4.
19. TYPES OF TIME COMPLEXITY
Best Case Time complexity
Exp(1) – Linear search/Binary search
Linear search, key=3
a[0]==key, T(n)=O(1)
Binary search, key=24
m=(0+4)/2 = 2
a[2]==key, T(n)=O(1)
3 5 24 45 78
20. TYPES OF TIME COMPLEXITY
Worst Case Time complexity
Exp(2) – Linear search/Binary search
Linear search, key=78 / 80
a[0]==key, T(n)=O(n) / O(n+1) ≈ O(n)
Binary search, key=78 / 80
m=(0+4)/2 = 2 …
a[2]!=key,…
finally T(n)=O(log2 𝑛) ….(*)
3 5 24 45 78
21. TYPES OF TIME COMPLEXITY
Average Case Time complexity
Exp(3) – Linear search/Binary search
Linear search, key=24
a[0]==key, T(n)=O((n+1)/2) ≈ O(n)
There are n cases that can occur, i.e. find at the first place,
the second place, the third place and so on up to the nth
place. If found at the ith place then i comparisons are
required. Hence the average number of comparisons over
these n cases is:
average = (1+2+3.....+n)/n = (n+1)/2
where the result was used that 1+2+3 ...+n is equal to
n(n+1)/2.
Binary search, key=5
m=(0+4)/2 = 2, m=(0+1)/2=0, m=(1+1)/2=1
a[1]==key, finally T(n) ≈ O(log2 𝑛) ….(*)
3 5 24 45 78